Question

The altitude of a triangle is increasing at a rate of 2000 centimeters/minute while the area of the triangle is increasing at a rate of 2000 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 8000 centimeters and the area is 96000 square centimeters?

Answer 1

A = bh/2 = 99000 = bh/2
h = 10000

198000 = 10000b
b = 19.8

A = bh/2
dA/dt = (bdh/dt + hdb/dt)/2

A' = (bh' + hb')/2

h' = 1500 cm/min
A' = 1000 cm²/min

1000 = (1500b + b'h)/2
2000 = 1500b + b'h

b' = (2000 - 1500b)/h


b' = (2000 - 1500*19.8)/10000

b' = db/dt = -2.77 cm/min n